There's no doubt that organised religion has stifled science, and still attempts to, to a degree. It's impossible to know whether the human race would have advanced considerably more without religion, but my guess is that it would.
It's not only religion that stifles science - scientists themselves often delay progress by immediately declaring innovative ideas to be 'impossible', and failing to carry out research, only to find years later they were mistaken.
Man, especially one with a closed mind, is an arrogant creature, convinced that he, personally, has the answers, even though he has no evidence. Closed minds always succeed in stifling scientific progress.